A Subtle Symmetry of Lebesgue's Measure

Creative Commons License

Uludag M., Ayral H.

JOURNAL OF THEORETICAL PROBABILITY, cilt.32, sa.1, ss.527-540, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s10959-017-0804-y
  • Dergi Adı: JOURNAL OF THEORETICAL PROBABILITY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.527-540
  • Anahtar Kelimeler: Farey tree, Modular group, Boundary, Measure, Lebesgue measure, Stern-Brocot tree, Calkin-Wilf tree, FUNCTION EXPLICIT SERIES, DYADIC PERIOD FUNCTION
  • Galatasaray Üniversitesi Adresli: Evet

Özet

We represent the Lebesgue measure on the unit interval as a boundary measure of the Farey tree and show that this representation has a certain symmetry related to the tree automorphism induced by Dyer's outer automorphism of the group PGL(2,Z). Our approach gives rise to three new measures on the unit interval which are possibly of arithmetic significance.